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The parabolic velocity profile in a fully developed laminar flow in a pipe is given by the following equation, -R (dP u(r) = 4u (dx Where R is the radius of the cylindrical pipe and r is the distance from the center (OsrsR). Using this equation (a) Why the pressure gradient must decrease in the flow direction, (b) Explain where the maximum velocity will occur, (c) Demonstrate that the maximum velocity of the fluid is given by 2 times of its average velocity.

The parabolic velocity profile in a fully developed laminar flow in a pipe is given by the following equation, -R (dP u(r) = 4u (dx Where R is the radius of the cylindrical pipe and r is the distance from the center (OsrsR). Using this equation (a) Why the pressure gradient must decrease in the flow direction, (b) Explain where the maximum velocity will occur, (c) Demonstrate that the maximum velocity of the fluid is given by 2 times of its average velocity.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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The parabolic velocity profile in a fully developed laminar flow in a pipe is given by the following equation, -R? ( dP u(r)=: 4µ (dx R Where R is the radius of the cylindrical pipe and r is the distance from the center (OsrsR). Using this equation (a) Why the pressure gradient must decrease in the flow direction, (b) Explain where the maximum velocity will occur, (c) Demonstrate that the maximum velocity of the fluid is given by 2 times of its average velocity.
Transcribed Image Text:The parabolic velocity profile in a fully developed laminar flow in a pipe is given by the following equation, -R? ( dP u(r)=: 4µ (dx R Where R is the radius of the cylindrical pipe and r is the distance from the center (OsrsR). Using this equation (a) Why the pressure gradient must decrease in the flow direction, (b) Explain where the maximum velocity will occur, (c) Demonstrate that the maximum velocity of the fluid is given by 2 times of its average velocity.
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